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On absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator. (English) Zbl 1241.35141

Summary: Absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator is proved provided that the magnetic potential \(A\) belongs to the space \(H^q_{\mathrm{loc}}\), \(q >1\), and the matrix potential \(\widehat V\in L^3_{\mathrm {loc}}\) is represented in the form \(\widehat V=\widehat V_0+\widehat V_1\), where \(\widehat V_0\) commutes and \(\widehat V_1\) anticommutes with the Dirac matrices \(\widehat \alpha _j\), \(j = 1, 2, 3\).

MSC:

35P05 General topics in linear spectral theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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